Solve for p (complex solution)
p=\frac{6x}{x^{2}+1}
x\neq -i\text{ and }x\neq i
Solve for p
p=\frac{6x}{x^{2}+1}
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{9-p^{2}}+3}{p}\text{; }x=\frac{-\sqrt{9-p^{2}}+3}{p}\text{, }&p\neq 0\\x=0\text{, }&p=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{9-p^{2}}+3}{p}\text{; }x=\frac{-\sqrt{9-p^{2}}+3}{p}\text{, }&p\neq 0\text{ and }|p|\leq 3\\x=0\text{, }&p=0\end{matrix}\right.
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px^{2}+p=6x
Add 6x to both sides. Anything plus zero gives itself.
\left(x^{2}+1\right)p=6x
Combine all terms containing p.
\frac{\left(x^{2}+1\right)p}{x^{2}+1}=\frac{6x}{x^{2}+1}
Divide both sides by x^{2}+1.
p=\frac{6x}{x^{2}+1}
Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.
px^{2}+p=6x
Add 6x to both sides. Anything plus zero gives itself.
\left(x^{2}+1\right)p=6x
Combine all terms containing p.
\frac{\left(x^{2}+1\right)p}{x^{2}+1}=\frac{6x}{x^{2}+1}
Divide both sides by x^{2}+1.
p=\frac{6x}{x^{2}+1}
Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.
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